How to convert RPM to linear speed

Written by paul travers| 13/05/2017

The linear speed of a given point on a rotating object can be worked out from its RPM. (Ryan McVay/Digital Vision/Getty Images)

"RPM" stands for "revolutions per minute" and describes how many times a spinning object revolves around a fixed point in one minute. In order to convert RPM to linear speed, you must first specify the distance of a point from the axis of a revolution. The rim of a wheel or the outside edge of a record, for example, covers far more distance than a point that is nearer the axis. If the distance from the axis is r, then the linear distance covered in 1 revolution = 2πr.

Measure the distance from the axis of rotation to the point whose linear speed you wish to determine. A 12-inch record, for example, would have a radius of 6 inches. The distance to the outside edge of the record would therefore be 6 inches.

Determine the RPM of the object. If the record is a 12-inch single, for example, it might spin at 45RPM.

Use 1 revolution = 2πr to work out the linear speed. Using the above example, 1 revolution = 2π6 = 37.699 inches. Every time the record revolves, a given point on the outside edge travels 37.699 linear inches. In 45 revolutions it would travel 45 x 37.699 = 1696.455 inches. This gives you a linear speed of 1696.455 inches per minute.

Convert to whichever units you wish to use. In the above example, you could divide the linear speed by 60 to give you the speed in inches per minute. You could multiply it by 2.54 to give you the speed in centimetres per minute.